Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21446975 | C2 | semidirect |
| 2. #21444860 | C2 | semidirect |
| 3. #21444758 | C2 | semidirect |
| 4. #21443846 | C2 | semidirect |
| 5. #21443822 | C2 | semidirect |
| 6. #21443751 | C2 | semidirect |
| 223. C61 | #12274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446975 | 2 |
| #21444860 | 2 |
| #21444758 | 2 |
| #21443846 | 2 |
| #21443822 | 2 |
| #21443751 | 2 |
| C61×#2828 | 2 |
| #12274 | 61 |